Question: Two new mathematics learning techniques are being tested. Twenty students were randomly selected ...

Two new mathematics learning techniques are being tested. Twenty students were randomly selected from a population. nA = 9 of them were randomly assigned to use technique A, and nB 11 of them were randomly assigned to use technique B. Each student spent 30 minutes learning the technique to which they were assigned, and then were asked to complete a task. The time to complete the task was recorded, in seconds. A shorter time indicates better mastery of the task. The data are below: TechniqueA : 23.1, 21.4,31.6,34.5,21.9,36.0,30.2,33.1,39.5 TechniqueB : 32.7,36.8,39.1,37.3, 40.3, 46.8, 41.4,53.0, 55.6,54.1,28.3 We wish to test: VS using a -0.05. (a) Graph the data as you see fit. Why did you choose the graph(s) you did and what does it (do they) tell you? Also calculate summary statistics relevant to the research question. (b) Use the bootstrap to perform the test, using B 10000 resamplings and set.seed(1). Display the histogram of your generated t values. Compute your tobs and a p-value. Make a reject or not reject decision. Finally, state your conclusion in the context of the problem (c) Use R to perform a two-group t test for means (i) assuming equal variance and then (i not assuming equal variance (Welch's T) and report the p values from each. Describe how the three p values are related. Explain how the histogram in part (b) and the summary statistics in part (a) hinted at this relationship

Show transcribed image textTwo new mathematics learning techniques are being tested. Twenty students were randomly selected from a population. nA = 9 of them were randomly assigned to use technique A, and nB 11 of them were randomly assigned to use technique B. Each student spent 30 minutes learning the technique to which they were assigned, and then were asked to complete a task. The time to complete the task was recorded, in seconds. A shorter time indicates better mastery of the task. The data are below: TechniqueA : 23.1, 21.4,31.6,34.5,21.9,36.0,30.2,33.1,39.5 TechniqueB : 32.7,36.8,39.1,37.3, 40.3, 46.8, 41.4,53.0, 55.6,54.1,28.3 We wish to test: VS using a -0.05. (a) Graph the data as you see fit. Why did you choose the graph(s) you did and what does it (do they) tell you? Also calculate summary statistics relevant to the research question. (b) Use the bootstrap to perform the test, using B 10000 resamplings and set.seed(1). Display the histogram of your generated t values. Compute your tobs and a p-value. Make a reject or not reject decision. Finally, state your conclusion in the context of the problem (c) Use R to perform a two-group t test for means (i) assuming equal variance and then (i not assuming equal variance (Welch's T) and report the p values from each. Describe how the three p values are related. Explain how the histogram in part (b) and the summary statistics in part (a) hinted at this relationship